[BP06] Feasible node colorings of trees with cardinality constraints

Résumé: Given a tree T with n vertices and three nonnegative
integers (n1,n2,n3) such that n1+n2+n3=n, our goal is to
find a 3-coloring of T such that each color class i contains
ni nodes i=1,2,3. Using a dynamic programming approach we
show that this problem can be solved in time O(n5 log n). We
also show that our algorithm can be adapted to the case of
k-colorings for fixed k.